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Index

A posteriori error estimates, 56, 92adaptive, 32admissible (kinematically), 25,41,66,183

admissible (solution), 27, 34admissible (statically), 25, 41, 66, 183admissible (thermodynamically), 23admissibility (notion of), 25, 32assemblage, 149, 154, 160, 162, 169,170,173

augmented Lagrangian, 52, 110, 159

Beam, 101, 178, 190,200bi-potential, 36bi-standard, 24,34-37, 43buc~ing, 177,189,202,204

Cauchy stress, 180, 195cohesion, 191, 195compact, 122conjugate gradient, 52, 200convergence, 39,44,49, 74,84,87,90,98,107,111,115,118,122,127,131,146,155,159,164,166,168,171

convex (strictly), 108, 109convex sweeping, 39, 43crack, 4, 202cyclic, 135cyclic jumps, 135

Damage, v, 4, 37, 52, 153, 177,202-204

decomposition (of domain), 149, 150,154, 160

delamination, 153, 204derivative (of Jaumann), 179, 180discretization (in time), 44, 117, 130,131, 141

dissipation (pseudo-potential), 12, 14,17,18,21

dual (function), 14, 17, 18, 76

Elastic domain, 14, 18equation of state, 16, 153, 192error in constitutive relation (CR), v,9, 24-26, 28-30, 32, 34-37, 99

error in dissipation, 9, 28, 29error indicators, 48, 92, 93, 127, 142Euclidean space, 1Euclidean transpose, 1

Fatigue, 135finite elements, 25, 32, 40, 48, 52,100,111, 117, 136, 138, 140, 145

first law (of thermodynamics), 10fluid, 37free energy, 4, 9, 10, 14, 18,25,28,33,35,56,69,92,100,193

friction, 36, 151, 152, 156, 163, 164,167

Gauss (points), 150gradient, 12,21, 179, 187, 190, 195,197

Hypercircle, 10, 29, 35hyperelastic (material), 101,107,110

Identification, 9incompressibility, 13, 16incremental (methods), 39, 52, 55indicator function, 14, 16-18,33,43,75

initial conditions, 2, 3, 5, 6, 25, 34,56, 141

initial value, 46, 74initialization, 58, 102, 107, 109, 115integration (cycles of), 136, 138integration (points of), 112, 136

220 Index

interface, 149, 151,152,154, 158,161,163-166,168,170,171,173

interfaces (examples ot), 151internal stress, 179, 183internal variables (models with), 9, 154

Jaumann strain rate, 177

Large deformations, v, vi, 4, 52, 177,178,182,187,189,192,199

Legendre-Fenchel, 12linearized, 111, 114local equations, 4, 45, 55-58, 108, 154,171,195,196,200

local error, 37

Material (formulation), vi, 183material (quantities), 177mesh, 32, 111metal forming, 178monotone (maximal), 75, 76, 78, 84, 87,90,91

monotone (strictly), 48-51, 88, 167

Newton, 39, 40, 47, 48, 52, 109-111,119,128,177

normal formulation, 9, 21-24, 29, 30, 32,34,41,43,56,102,149,170

notation, 1, 10, 11, 15,27,29,35,40,49,63,77,79,80,88,90,95,102,145,151,155,156,171,172,179

Parallel, 48, 127, 128, 149, 150, 160parallelism (degree ot), 128,149,150partitioning, vi, 56, 58, 108, 112, 136,150,153,154,171

perfect links, 159, 163, 167performance, 52, 55, 121, 125periodic, 135, 136, 139plasticity (perfect), 16, 43point environments, 44Prandtl-Reuss, 14, 15, 17, 125preliminary phase, 118, 119, 127, 130,131, 146

principle of virtual power, 3, 4, 7

Quasi-Newton, 52, 129

Radial loading, 111, 114, 119, 128,191,199

rate (of deformation, strain), 3,10,13,32,66,177,179,180,182,183,187,191,197

rate (of stress), 41Rayleigh quotient, 120, 121, 123regularity, 4,12,37,74,79,163

Second law (of thermodynamics), 11shell, 190singularity, 4small disturbances, 1, 3, 4, 10, 52, 149,177,180,187,189,196,197,200

stability, 5, 6, 32, 34, 36, 44, 191standard (model), 18,26,27,99stress formulation, 72sub-differential, 12, 21, 88

Temperature, 19,24,131trace, 1, 18, 32

Uniqueness, 1, 4-6, 19, 70, 74, 91,168

update, 37

Velocities (problem in), 117, 191

Mechanical Engineering Series (continued from page ii)

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